Essential Math, Percentage, and Geometry Calculation Guide
Quick formulas for percentages, averages, geometric shapes, and algebraic ratios.
Mathematics is the language of problem solving. Whether you need to determine percentage markdowns, compute geometric volumes, or calculate weighted grade averages, having reliable mathematical equations at your fingertips makes complex problems simple and error-free.
A positive result represents an increase, while a negative result represents a decrease. Geometric formulas include Circle Area = πr² and Triangle Area = 0.5 × base × height.
Scenario: An online product price changed from $80 down to $60 during a seasonal sale.
- Old Value: $80
- New Value: $60
- Difference = 60 - 80 = -20
- Divide by original = -20 / 80 = -0.25
- Multiply by 100 = -0.25 × 100% = -25%
- A 50% decrease followed by a 50% increase does not return to the original number ($100 → $50 → $75).
- When calculating averages with outliers, consider median values instead of arithmetic mean.
- Always follow the standard order of operations: Parentheses, Exponents, Multiplication & Division, Addition & Subtraction (PEMDAS).
- Use our geometry tools to calculate perimeter, area, and volume with exact mathematical constants.
Put the formulas above into practice with these free tools:
Percentage Calculator
Find X percent of any number.
Percentage Change Calculator
Increase or decrease between two values.
Average Calculator
Mean, median, and sum of a list of numbers.
Pythagorean Theorem Calculator
Hypotenuse and area of a right triangle.
Circle Calculator
Area, circumference, and diameter from the radius.
Rectangle Calculator
Area, perimeter, and diagonal of a rectangle.
Quadratic Equation Solver
Real roots of ax² + bx + c = 0.
GCD and LCM Calculator
Greatest common divisor and least common multiple.
Standard Deviation Calculator
Mean, variance, and standard deviation of a data set.
Ratio and Proportion Calculator
Solve a : b = c : x.
Triangle Area Calculator
Area and perimeter from three side lengths.
Combinations and Permutations Calculator
Count ways to choose or arrange items.
What is the difference between mean, median, and mode?
Mean is the sum of values divided by count; median is the middle value in an ordered set; mode is the most frequently occurring value.
How do I calculate percentage of a number quickly?
Multiply the number by the percentage written as a decimal (e.g. 15% of $80 is 80 × 0.15 = $12).
What is the Pythagorean theorem?
In any right-angled triangle, a² + b² = c², where c is the hypotenuse opposite the 90-degree right angle.